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A b s t r a c t. The paper presents experimentally registered
temperatures occurring in RC grouped silo bins for grain, correspon-
ding to winter operation period in Polish climate conditions. A new
generation wireless computerized measurement system was
applied, based on the use of telemetric transceivers operating in
intelligent radio network. On the basis of experimental temperature
distribution, numerical analysis of the hoop thermal stresses and
bending moments in reinforced concrete silo battery subjected to
grain pressure and thermal gradient was carried out. In the ana-
lysis the numerical model of silo wall with interaction between wall
structure and stored particulate solid was applied which had pre-
viously been developed and validated on a stand-alone ferrocon-
crete silo bin model.
K e y w o r d s: temperature fields, thermal stresses, silo bat-
tery, structural analysis, finite element method
INTRODUCTION
Thermal loads on silo wall should be obligatory consi-
dered in design of silo structures, and the influence of tem-
perature fields should be carefully studied with respect to the
model of thermal effects and idealized model of silo wall
structure. The effects on structures of grouped silos in grain
Elevators and the requirements for their structural analysis
are not specified in recent codes of design (EN 1991-4:2006;
PN-B-03262:2002; AS-3774-1996).
Previously the problem of thermal effects in RC cylindri-
cal free standing silos was analysed in Canada (Muir et al.,
1989), South Africa (Blight, 1990) and last time in Poland
(£apko, 2005; £apko and Prusiel, 2001; 2003).
The paper presents some results of experimental and
computational analysis of temperature fields and thermal
effects occurring in RC grouped grain silos (arranged as 2 x
2 cylindrical bins) subjected to thermal loads, elaborated
using own numerical model taking into account the
interaction between wall structure and particulate solids ‘en
masse’ (£apko et al., 2001; £apko and Prusiel, 2001).
MONITORING OF THERMAL LOADS AND THERMAL
STRESSES IN GROUPED SILOS FOR GRAIN
The temperature distributions in a real silo wall in a grain
Elevator were monitored using a new generation wireless
system equipped with telemetric radio modules (a scheme of
such a system is presented in Fig. 1) providing the pos-
sibility of testing the silo structure by measurement of me-
chanical stresses, deformations, displacements or tempera-
tures – depending on sensors used.
Bi-directional wireless monitoring was carried out by
radio transceivers operating with strain gauge measurement
circuits (£apko and Ko³³¹taj, 2003). All the measurements
are performed over the radio, therefore the telemetry
modules are equipped with a number of functions (zeroing,
scaling, calibration, filtration) using the wireless technique.
The system is equipped with a special algorithm of data
transmission. The computer program is implemented into
microprocessor system in the transmission modules. The
system was specially designed for operation with low level
of signals in strain gauge circuits and provided with the
following functions:
– running measurements – with displayed values for all
sensors (without registration),
– on-line measurement (with computer registration) and
displayed values for chosen channels,
– off-line registration (without main station),
– detection of strain gauge damage (shorting of the strain
gauges),
– setting of sampling frequency.
Using the above mentioned wireless technique the
monitoring of reinforced concrete grouped silo, consisting
of a battery of 2 x 2 cylindrical silos in the grain Elevator in
Bialystok (Poland), was conducted during a long winter
period. The tested silo bins, K–9 and K–11, as seen in the
Int. Agrophysics, 2006, 20, 301-307
Analysis of thermal effects in grouped silos of grain elevators
A. £apko and J.A. Prusiel*
Institute of Civil Engineering, Bia³ystok University of Technology, Wiejska 45, 15-351 Bia³ystok, Poland
Received July 11, 2006; accepted September 27, 2006
© 2006 Institute of Agrophysics, Polish Academy of Sciences*Corresponding author’s e-mail: [email protected]
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wwwwwwwww...iiipppaaannn...llluuubbbllliiinnn...ppplll///iiinnnttt---aaagggrrroooppphhhyyysssiiicccsss
cross section in Fig. 2, were fully filled with particulate solid
(wheat) being in the storing phase. The main geometric data
of the silo bins from the grouped silo were as follows:
– internal diameter dc = 8 m,
– total height H = 26 m,
– wall thickness t = 0.2 m,
– length of contact zone between bins L = 2.4 m.
Digital temperature sensors type DS18B20 were loca-
ted at the outer surface of concrete wall along the perimeter,
at the level of 8 m above the ground of the silo battery. The
temperature test points were distributed in horizontal distan-
ce of the bin perimeter with central angle 45°as shown in
Fig. 2. The electric resistance strain gauges were localised at
the silo height on uncovered outer steel reinforcement bars
(with diameter of 12 mm) and located on mean average
distance of 150 mm.
The strain test points were localised on the silo bin K–9
at selected four levels situated on two vertical lines A and C
(on the levels of 12, 10, 8 and 6 m above the ground see Fig. 2)
along vertical cracks observed on the concrete surface.
Example diagrams of one week temperature registration
(at test points B–8, C–8, D–8 and E–8 – as shown in legend)
are presented in Fig. 3a. Changes of thermal hoop strains in
outer steel bars (at a few selected test points), corresponding
to the registered temperature changes, are given in Fig. 3b. It can
be clearly seen that the diagrams of temperature and thermal
stresses are coupled eg for each phase of temperature drop
we observe increase of tensile thermal stresses in the rein-
forcement and vice versa.
SIMULATION OF TEMPERATURE CHANGES
IN THE SYSTEM: SILO WALL STRUCTURE – STORED
BULK SOLID
During the investigations temperature changes on exter-
nal surface of wall perimeter were monitored. For evalua-
tion of corresponding temperature changes on the wall thick-
ness the numerical program based on the Finite Difference
Method (FEM) computational procedure was used. The
program is based on the principles of heat transfer and
moisture migration in cylindrical systems (£apko and
Prusiel, 2001; 2003), as shown in Fig. 4.
The designed system was subdivided into basic
cylindrical layers (RC wall structure and grain) and the
following input data were introduced:
– thickness and number of basic layers,
– initial temperature and moisture of layer,
– thermal conductivity characteristics,
– specific heat,
– density of material,
– characteristics of vapour permeability,
– isotherm of sorption of considered material.
302 A. £APKO and J.A. PRUSIEL
Fig. 1. Cylindrical silo bin structure during monitoring: a) scheme of wireless transmission: 1– transceivers, 2 – main station connected
with computer; b) view of tested silo bin K–9 in Bia³ystok Elevator.
K-9
a b
Fig. 2. Location of temperature test points on the surface of grain
silo battery perimeter.
ANALYSIS OF THERMAL EFFECTS IN GROUPED SILOS OF GRAIN ELEVATORS 303
Fig. 3. Temperature distributions on silo battery perimeter (December 2002) (a) and corresponding thermal strain changes in reinforcing
steel at selected test points (b) (£apko, 2005).
Time (h)
Str
ains
of
stee
l(‰
)
b
Time (h)
Tem
per
ature
(�C
)
a
Fig. 4. Assumptions for the numerical computation of temperature in the system: silo wall – bulk solid (£apko and Prusiel, 2001);
T = f(r) temperature function against silo wall radius.
Temperature changes predicted numerically along the
silo bin radius during 19 h long phase of dropping winter
temperature (see Fig. 3) are shown in Fig. 5.
External temperature changes, �Te, needed in the simu-
lation were taken from experimental works and on this basis
the internal surface wall temperature changes, �Ti, were
predicted (Fig. 6).
From here the thermal effects components for consi-
dered silo battery (linear thermal gradient, �Tg, and uniform
temperature changes, �Tm) were established for some
selected points on silo wall circumference. The respective
results are given in Table 1.
FEM ANALYSIS OF THERMAL FORCES IN SILO WALL
The structure of a grouped silo is very complex and the-
refore the known solutions for evaluation of thermal stresses
in a freestanding cylindrical silo cannot be used even for
symmetrical loads.
The FEM was used in structural analysis of considered
silo battery subjected to grain pressure and previously
predicted thermal effects. In the analysis the discrete
numerical model of grouped silo, taking into account
interaction between wall structure and stored particulate
solid, was applied. This model was previously developed
304 A. £APKO and J.A. PRUSIEL
-16.0
-12.0
-8.0
-4.0
0.0
4.0
8.0
12.0
16.0
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75
0 19 h
WHEAT
Fig. 5. Temperature distribution along the radius of silo bin.
Tem
per
ature
(�C
)
Design points at the bin radius (cm)
-16,0
-14,0
-12,0
-10,0
-8,0
-6,0
-4,0
-2,0
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160
[deg]
Tem
per
atu
re[0
C]
To Tm
Te Tg
D8 C8 B8 A8
Fig. 6. Wall temperature distribution over the wall perimeter taken in computer simulations; To, Te – external surface temperature at the
start and the end of monitoring, respectively, Tm – mean wall temperature; Tg – temperature difference at the wall thickness.
Angle (�)
Tem
per
ature
(�C
)
Test points
WALL
and validated on a silo model (£apko and Prusiel, 2001;
2003). Numerical scheme of analysed horizontal cross-
section of silo battery structure is presented in Fig. 7. The con-
tact between adjacent silo bins in grouped silo was modelled
assuming real increase of wall stiffness in this zone.
The numerical FEM model of the 2 x 2 bins silo battery
is based on the shell plate Finite Elements having radial
oriented constrains in the nodes modelling the bulk solid
stiffness in the nodes. The elastic stiffness characteristic, C,
of stored grain in silo bin was defined considering the equili-
brium of deformations of elastic ring in contact with elastic
bulk solid core separated from cylindrical silo wall with the
diameter, dc, and the wall thickness, t. From the equilibrium
of strains we obtain:
CE
d t
s
c s
�� �05 1. ( )( )�
, (1)
where: Es and � s are modulus of given bulk solid and its
Poisson ratio, respectively.
The effective modulus of given particulate solid can be
determined experimentally or predicted by indirect asses-
sment depending on unit weight, �, of stored solid.
European Standard final draft (EN 1991-4: 2006)
proposes the following empirical formula for evaluation of
unloading effective modulus of particulate solid:
E psU vft� � , (2)
where: pvft – vertical stress due to bulk solid pressure at the
base of the vertical walled section, � – modulus contiguity
coefficient.
In the absence of experimental data from tests, the
modulus contiguity coefficient, �, may be estimated as:
� �� 7 3 , (3)
where: � – unit weight of the stored solid in kN m-3
; for
wheat we have � = 7.8 kN m-3
.
The value of coefficient, �, may alternatively be taken as
70 – for dry agricultural grains, 100 – for small mineral
particles, and 150 – for large hard mineral particles.
The vertical stress in Eq. (2) may be computed from
formula based on Janssen pressure:
pp
KY zvft
hoj� ( ) , (4)
where:
p Kzho o� � ,
zK
A
Uo �
1
,
Y z ej
z
zo( )� �
�
1 ,
where: – coefficient of friction between silo wall and bulk
solid, K – characteristic value of the lateral pressure ratio,
z – depth below the equivalent surface of the solid, A – plan
cross-sectional area of the silo, U – internal perimeter of the
plan cross-section of the silo.
Assuming the standard approach for the needs of
numerical analysis we obtained in the paper:
�� �7 78 1523. ,
pvft � 62.12 kN m-2
,
EsU � 94. MPa.
ANALYSIS OF THERMAL EFFECTS IN GROUPED SILOS OF GRAIN ELEVATORS 305
�T Thermal effects (�C)
H-G F E D C B A
�Te -6.1 -13.6 -11.5 -10.7 -8.1 -7.6 -7.5
�Ti -1.6 -1.6 -1.5 -1.6 -1.3 -0.6 -1.0
�Tg -4.5 -12.0 -10.0 -9.1 -6.8 -7.0 -6.5
�Tm -3.85 -7.6 -6.5 -6.15 -4.7 -4.1 -4.25
*H, G, F, E, D, C, B, A – temperature test points (see Fig. 2).
T a b l e 1. Thermal loads on silo battery wall from monitoring and numerical analysis
Fig. 7. Scheme for FEM analysis of silo battery using discrete
model of interaction between wall structure and bulk solid.
The numerical FEM scheme of considered grouped silo
was modelled with 4096 finite wall elements having
dimensions of 800 x 800 mm and the same number of
constrains modelling the core of grain. The silo battery
consisted of four cylindrical bins made of concrete class
B20. Thermal effects were assumed to be linear across the
wall thickness and not uniform on silo battery perimeter
(Fig. 2), as given in Table 1.
Example diagrams of thermal stresses and bending
moments in considered silo bin K–9 structure (for outer arch
of the wall), assuming the experimentally registered daily
thermal effects, are presented in Fig. 8a (thermal uniform
stresses on the wall thickness) and in Fig. 8b (thermal ben-
ding moments). The diagrams marked with (C=0) denote the
results of numerical tests neglecting interaction between the
wall structure and bulk solid stored (for the stiffness cha-
racteristic parameter C=0).
The comparison of numerical tests obtained from
numerical FEM analysis using the model with interaction
(C�0) and classic FEM model without interaction (for C=0)
shows significant influence of the bulk solid stiffness on the
hoop thermal stresses in the silo wall sections.
Assuming the reinforced concrete section of silo wall
for the computed uniform hoop thermal stress, T , and ther-
mal bending moment, MT, the following formula for evalua-
tion of thermal stresses, sT , in outer hoop reinforcement
can be used:
sTT
Ts
cm
M
W
E
E� �
�
�
�
�� , (5)
where: W – is the silo wall section modulus and Es/Ecm – is
the ratio of steel and concrete moduli.
Taking the values of MT and sT from diagrams (Fig. 8)
and assuming for cracked wall concrete modulus Ecm =
13.5 GPa, for steel modulus Es = 210 GPa and wall thickness
t = 0.2 m in the wall cross-section (for the angle � = 150�) we
obtain the value of thermal stresses in hoop tension
reinforcement:
sT � 82. MPa . (6)
To compare this value with the thermal stress changes
registered during silo wall monitoring (see Fig. 3b for test
point C-8 at the considered level of 8 m of silo wall height)
for the measured change of steel strains, � �s, related to
daily temperature drop we obtain:
�s s sE� � � �� 0047 210 99. . MPa. (7)
The discrepancies of thermal stresses in hoop reinfor-
cement of silo battery due to daily drop of ambient tempe-
rature predicted experimentally and taken from FEM ana-
lysis are not significant and validate the proposed numerical
approach for silo battery structural analysis.
CONCLUSIONS
1. Experimental analysis of temperature distribution
and thermal effects on real silo batteries can be very effi-
ciently carried out using new generation wireless moni-
toring system.
2. Structural analysis of silo battery structure under bulk
solid pressure and non-uniform thermal actions proved that
the thermal forces and moments in silo wall sections should
be evaluated taking into account the numerical FEM silo bin
model assuming the interaction between wall structure and
bulk solid.
3. It can be clearly seen from numerical analysis that
short time (daily) winter temperature drop influences hoop
stresses resulting from bulk solid pressure in the wall section
of silo battery and this effect must be considered in design of
silo battery structure.
306 A. £APKO and J.A. PRUSIEL
a
Ther
mal
stre
ss(k
Nm
-2)
Angle (�)
Fig. 8. Selected diagrams for outer arch of silo bin K–9 at the level
of 5.5 m: a) uniform thermal hoop stresses in concrete, b) thermal
hoop moments.
Ther
mal
hoop
mom
ents
(kN
mm
-1)
Angle (�)
b
REFERENCES
AS-3774-1996. Australian Standard. Loads on bulk solid con-
tainers. Published by Standards Australia.
Blight G.E., 1990. Temperature surcharge pressures in rein forced
concretre silos. Powder Handling and Processing,
2, 4, 303-305.
EN 1991-4: 2006. Eurocode 1 – Actions on structures – Part 4:
Silos and tanks.
£apko A., 2005. Thermal fields in grain during storage – their
sources and effects on silo structures reliability. Int.
Agrophysics, 19, 141-146.
£apko A. and Ko³³¹taj J., 2003. The wireless technique of
examination of silo wall structures during operation. Proc.
4th Int. Conf. Conveying and Handling of Particulate
Solids. Budapest, Hungary, 27-30 May, 1, 6.77-6.82.
£apko A., Nikitin V., Prusiel J.A., and Kowalczyk R., 2001.
Prediction of temperature fields and thermal forces in
cylindrical shell of silo chamber. Proc. 4th Int. Cong.
Thermal Stresses, Osaka, Japan, 537-540.
£apko A. and Prusiel J.A., 2001. Studies on thermal actions and
forces in the cylindrical storage silo bins. Handbook of
Conveing and Handling of Particulate Solids. Elsevier,
Amsterdam.
£apko A. and Prusiel J.A., 2003. Experimental and theore-
tical analysis of thermal effects in full – scale grain silo
battery. Proc. 5th Int. Cong. Thermal Stresses and Re-
lated Topics Blacksburg, Virginia, USA, 8-11 June, 1, MM-
2-1-1-MM-2-1-4.
Muir W.E., Jayas D.S., Britton M.G., Sinha R.N., and White
N.D.G., 1989. Interdyscyplinary grain storage research.
Powder Handling and Processing, 3, 281-295.
PN-B-03262: 2002. Reinforced concrete silos for granular
substances. Statistic calculations and drafts (in Polish).
Polish Standard Committee, Warsaw.
ANALYSIS OF THERMAL EFFECTS IN GROUPED SILOS OF GRAIN ELEVATORS 307